PHYSICS SEMINAR
Black hole free energy during charged collapse
Hugues Beauchesne, B.Sc. and world traveler!
Bishop's University
Friday, November 18, 2011
1:30 p.m.
N315
Recent work on the 4D (3+1) and 5D collapse of matter to a black hole in isotropic coordinates have provided numerical evidence for associating the negative of the gravitational Lagrangian at late times of the collapse to the free energy of the Schwarzschild black hole. We verify numerically this association for the case of gravitational collapse of charged matter (a complex scalar field) in isotropic coordinates. We first derive the equations of motion and obtain expressions for the conserved quantities: the ADM mass M and the total charge Q. We then explain how the initial states are obtained numerically. After imposing appropriate boundary conditions, the metric and matter fields are evolved and undergo collapse to a black hole. The (electric) potential is constant inside in accord with the presence of a charged shell. We track the Lagrangian and show that at late times it matches closely the free energy of the Reissner-Nordström black hole.
